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Mesas and Mammoths

The Atlatl: A Doorway to the Study of Dynamics
The lever is one of humanity's oldest tools. With a long pole and a stone acting as a fulcrum, our ancestors were able to lift heavier objects. The atlatl is another ancient device based on similar principles of leverage, in this case, to amplify throwing capability.

Atlatl dart with bone foreshaft and Clovis point

Atlatl dart with bone foreshaft and Clovis point.

The ability to throw a weapon or hunting projectile far and with accuracy is related to the speed of the projectile when released by the hunter. After the projectile leaves the hunter's control, gravity will dictate the resulting path.

The hunter's challenge is to achieve the highest speed possible. The kinetic, or moving, energy of a projectile increases with the square of the increase in the tangential velocity, as explained in the following equation:

kinetic energy = 1/2 x (mass) x (velocity)2

So how does an atlatl increase throwing speed? First, let's review the three stages involved in throwing a spear without an atlatl. Imagine the hunter is a three - stage rocket launcher. In the first stage, the arm rotates around the shoulder. In the second stage, the forearm rotates around the elbow. In the third stage, the hand rotates at the wrist. The spear is accelerated by each of these rotational motions.

Let's consider the third stage, when the hand is rotating at the wrist. The distance from the slot between the thumb and index finger to the wrist joint is about six centimeters. When we put an atlatl in the hand, the distance between the wristjoint and the end of the atlatl is 60 centimeters. Even though the rate of rotation of the wrist, and thus the angular velocity, remains the same, the throwing velocity increases in proportion to the distance from the point of rotation (radius of rotation). Thus the throwing speed at the end of the atlatl is 10 times that of the throwing speed of the hand alone. The following equation describes this effect:

Depiction of atlatl and spear being thrown.

tangential velocity = angular velocity x radius of rotation

If the angular velocity remains constant, the resulting tangential velocity is directly proportional to the radius of rotation.

Back to our atlatl. Remember that energy increases with the square of the tangential velocity. Thus, while we have a tenfold increase in velocity, we derive a hundredfold increase in energy.

Atlatl dart with wooden foreshaft and Folsom point

Atlatl dart with wooden foreshaft and Folsom point. The point is hafted to the foreshaft with "twine" made of animal sinew.

Angular Velocity Experiment
By Steve Newman, Environmental Engineer, NASA

Objective: To demonstrate the meaning of "angular velocity" and show students that for the same angular velocity objects may have greatly different tangential velocities.
For this activity, you will need

  • a 10-meter tape measure,
  • chalk,
  • a clipboard and paper,
  • and string.

Procedure: The students should work together to lay out two concentric circles on the blacktop, one with a 60-centimeter radius, the other with a 6-meter radius. To draw the circles, attach a piece of chalk to one end of a 60-centimeter length of string. Have a student hold the other end of the string, while a second student holds the chalk, pulls the string taut, and walks around marking the circle on the blacktop. Draw a single radius line. Repeat the process with a 6-meter length of string. Extend the radius from the smaller circle to the edge of the larger circle.

Position two students on the radius line, one on each circle, with a third student at the center of both circles. Cut a length of string that will pull taut between the student in the center and the one on the outer circle. The two students on the circles will run a lap, with the student on the inner circle keeping pace with the taut, circling string. Each runner completes the lap in the same amount of time. Who is moving at a higher velocity?

Of course, they are moving at the same angular velocity, but while angular velocity is identical, it is abundantly clear that the runner on the larger circle is moving much faster. That student has a tangential, or "around the circle," velocity roughly 10 times greater than the tangential velocity of the runner on the inner circle. This relationship can be expressed using the equation:

tangential velocity = angular velocity x radius of rotation

Photo of atlatl and spear being thrown.
Joseph H. Bailey and Larry Kinney, National
Geographic Society
Whiplash force adds lethal efficiency to spears thrown with an atlatl, a device often used by prehistoric hunters. Holding a grooved atlatl in his left hand, Dennis Stanford, Curator of Anthropology at the Smithsonian Institution, fits the spear's flint-tipped foreshaft into the the main shaft into the main shaft before loading the butt into the groove. To throw, Stanford swings it back and then forward over his head, snapping his wrist at the moment of release like a baseball pitcher, as shown in this nighttime multiple exposure.

Bicycle Kinetic Energy and Velocity Test
To demonstrate that the energy of a moving object (mass) greatly increases with small increases in speed.
For this activity you will need

  • bicycles (preferably equipped with pedal brakes and speedometers),
  • bicycle helmets,
  • a 100-meter tape measure,
  • a stopwatch,
  • chalk,
  • a clipboard and paper,
  • and a calculator.

Procedure: First, lay out the test range. On blacktop, draw two parallel chalk lines three meters apart. Draw a third line six meters beyond the second to mark the point where the bicyclists should apply the brakes. Ensure that there is a clear path of approximately 45 meters to allow students to reach a constant speed for their approach.

Next, assign the following student roles: velocity timer, velocity mark announcer, velocity data recorder, two-member stopping-distance measurement team, stopping-distance data recorder, and one or more bicycle "test pilots."

Have a helmeted test pilot pedal in a straight path at a constant speed and then quickly apply the brakes as the student crosses the third chalk line. The bicycle's actual speed will be determined by the velocity measurement team—the velocity mark announcer shouts out as the bicycle's front wheel reaches the first chalk line, alerting the velocity timer to start the stopwatch. The velocity timer stops the watch as the bicycle's front wheel reaches the second chalk line. The velocity data recorder notes the time and calculates the velocity using the following equation:


(The velocity will be expressed in terms of meters per second. Let students convert the figure to kilometers(km) per hour(h).)
The test pilot continues up to the third chalk line, then applies the brakes. The stopping-distance team then swings into action and measures the skid length or stopping distance. The stopping distance will be proportional to the energy required to stop the vehicle.

For example, at a speed of 8 km/h the bicycle's kinetic energy equals 1/2 m (8 km/h)2, while at 16 km/h the kinetic energy would be 1/2 m (16 km/h)2. At 16 km/hr it will take roughly four times the distance to stop the same vehicle than it would at 8 km/h, if we assume that braking energy is proportional to stopping distance. Do this experiment four or more times for each bicyclist at each speed, providing the class with a perspective on variability in experimental data and the use of the average to describe an experimental result. Students can calculate the average stopping distance and average speeds for each bicyclist. They can also plot individual trial run data on a graph of velocity versus stopping distance. The stopping - distance data for each test pilot should be labeled with the same symbol. The stopping distance should vary with the square of velocity for each individual test pilot where it is reasonable to assume mass does not change significantly between each run.

Ask students to identify sources of experimental variation, such as differences in braking points, braking pressure, and the surface friction. Experimental results will also be affected by the accuracy of the velocity timer and the stopping-distance measurement team.

Can you think of other sources of experimental variation? Discuss the use of large samples, and how the average value can be used to "smooth out" these experimental sources of variation and better reveal the underlying relationship between processes being measured or characterized.
 Note: Please take all necessary safety precautions if you choose to do this activity.

A Classification Activity
Students will use pictures of Paleoindian artifacts as they classify objects based on attributes and discover that the classification system used depends upon the question being asked of the data.
Have each student put one of his shoes into a pile. Have students divide the shoes into smaller piles based on color, then size, then style. Define attributes as the characteristics or properties of an object. Discuss how students have classified their shoes based on these attributes. What other attributes could they use?

We classify objects almost automatically in our everyday lives. We organize our clothes into such categories as clothes for school, dress-up occasions, play, and work. To do this, we choose to emphasize certain attributes and ignore others, because we cannot take all attributes into account at one time.

Classification of data is an important part of any scientific study, including archaeology. Scientists must categorize data based on various attributes to reduce their complexity and to examine the relationships between types of data. For example, it is not possible to compare a leaf from one type of deciduous tree with a leaf from every other deciduous tree. Instead, we categorize types of leaves within a certain range of variation as being in the same category. One category can then be easily compared with another.

Photo of pre-historic stone tools
Peter A Bostrom, Lithic Casting Lab

Divide students into groups of four or five and give each group a collection of about a dozen small stones. Have each group organize the stones into categories and then explain their classification scheme. Compare and contrast each group's scheme. Which classification is the best? Explain to your students that one classification scheme is not "better" than another. The utility of a given scheme depends on what the classifier wants to know.

To simulate how an archaeologist applies classification to his research, repeat this exercise using the Paleoindian artifacts pictured here. Photocopy the set of tools for each group, or as a preliminary activity, have students replicate some of the artifacts. Papier-mâché, carved plastic, or a low-temperature oven-hardened modeling compound are easy to use and can be painted to represent different raw materials. Have students classify the artifacts into groups. How might these objects have been used? How many sizes of stone tools are there? How many different shapes of tools are present? If you have replicated the artifacts, ask, How many different raw materials were used to make these artifacts? Students will find that they must reclassify the objects in order to answer different questions. As well, one artifact may be useful in answering several questions.

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